FLIGHT DYNAMICS MODEL OF A LARGE TRANSPORT AIRCRAFT

Novel breathing motion model for radiotherapy

Parameterization of group of rotations of Euclidean three-dimensional space applied to integration of rigid body motion equations

Identification modeling of ship nonlinear motion based on nonlinear innovation

On horizontal nondeformable ground, we consider the movement of a road train consisting of a biaxial tractor car and triaxial semitrailer treated as solid bodies. Based on the Lagrange’s equations of the second kind, we develop a nonlinear mathematical model of its plane motion, using the position of the fifth-wheel coupling and rotating angles of the tractor and semitrailer body as generalized coordinates. We analyze and linearize the constructed system of equations and obtain a linear mathematical model describing the small lateral displacements and rotations of the elements of a road train when it is moving at a high longitudinal speed, small jackknifing angle, and small rotation angle of the steering wheels. Using the equivalent transformations of the obtained system of equations, we construct a state-space linear model of the lateral motion of the road train. A comparative analysis of the use of linear and nonlinear models to describe the road train’s motion, carrying out standard maneuvers, is performed. It is shown that, if the restrictions are satisfied, then the results of nonlinear and linear model usage are quite close to each other and sufficiently well agree with the results of the field tests. The developed model, unlike the already known ones, is fairly simple (linear). Further, it could be used for an analytical synthesis of the control laws for the lateral component of the motion of road trains.

This paper outlines the mathematical motion model of the research spacecraft that uses solar sail instead of an engine and a propellant. The mathematical motion model for solar sail spacecraft is formulated and described. The work considers the mathematical motion model within the heliocentric system of coordinates. The best way to assess the reasonableness of the mathematical model is the using model in motion simulation process. On the basis of the formulated mathematical model the special software complex for interplanetary transfer simulation is developed. Especially, the mission of the transfer of the spacecraft from the Earth’s orbit to the potentially hazardous asteroid is simulated. The obtained results during simulation demonstrate correctness and feasibility of the considered mathematical motion model.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Nonlinear modelling of curvature by bi-linear metamodelling

Random runway roughness effect on the dynamic response of an aircraft with landing gears has been investigated using nine degree of freedom nonlinear mathematical model. The developed mathematical model incorporates nonlinear characteristics of air spring stiffness, landing gear damping, tire stiffness and damping of the oleo pneumatic main landing gears and nose gear. Equation of motion for aircraft and each landing gear have been written considering heave, pitch, roll of aircraft and three vertical motions of landing gears respectively for landing response analysis. The equations for longitudinal motion of each landing gear are also written from the mathematical model will be helpful for longitudinal dynamics. The aircraft touchdown and roll on with variable decent velocities on Grade E random runway represented by nonstationary random process. The excitation of different grades of random runway can be considered as stationary random process when the aircraft landing at constant sink velocity. This work mainly focused on finding the dynamic responses of the aircraft such as heave, pitch, roll acceleration, vertical forces and all the three landing gears vertical vibration levels while landing on random runways. The active landing gear system performance is compared with passive landing gear system by numerical simulation in MATLAB/SIMULINK. The investigation using nonlinear model predicted that the effect of active control landing gear provides significant reduction in vibration levels and vertical reactions during landing at various vertical velocities on random runways. To validate the above mathematical model a multi-body dynamics (MBD) model has been simulated in ABAQUS/CAE and the dynamic responses of landing gear forces are compared with those obtained from the nonlinear mathematical model. The nonlinear model responses are also compared with the results of other authors. This study is more useful to adopt active control landing gear in the aircraft to reduce the landing loads transmit on aircraft structure and landing gears due to landing impact. The reduction of vibration levels and vertical forces by the active system increase the fatigue life of landing gears and structural life of airframe.

Analysis of volatile organic compounds (VOCs) in breath specimens has potential for point of care (POC) screening due to ease of sample collection. While the electronic nose (e-nose) is a standard VOC measure across a wide range of industries, it has not been adopted for POC screening in healthcare. One limitation of the e-nose is the absence of mathematical models of data analysis that yield easily interpreted findings at POC. The purposes of this review were to (1) examine the sensitivity/specificity results from studies that analyzed breath smellprints using the Cyranose 320, a widely used commercial e-nose, and (2) determine whether linear or nonlinear mathematical models are superior for analyzing Cyranose 320 breath smellprints. This systematic review was conducted according to the guidelines of the Preferred Reporting Items for Systematic Review and Meta-Analyses using keywords related to e-nose and breath. Twenty-two articles met the eligibility criteria. Two studies used a linear model while the rest used nonlinear models. The two studies that used a linear model had a smaller range for mean of sensitivity and higher mean (71.0%–96.0%; M = 83.5%) compared to the studies that used nonlinear models (46.9%–100%; M = 77.0%). Additionally, studies that used linear models had a smaller range for mean of specificity and higher mean (83.0%–91.5%; M = 87.2%) compared to studies that used nonlinear models (56.9%–94.0%; M = 76.9%). Linear models achieved smaller ranges for means of sensitivity and specificity compared to nonlinear models supporting additional investigations of their use for POC testing. Because our findings were derived from studies of heterogenous medical conditions, it is not known if they generalize to specific diagnoses.

In this paper, a fractal–fractional mathematical model of convective fluid motion in rotating cavity is investigated inside the ellipsoid with inhomogeneous external heating. The fractal–fractional differential operators namely Caputo, Caputo–Fabrizio and Atangana–Baleanu $${\mathcal{D}}_{\tau }^{{\epsilon }_{1},{\tau }_{1}}$$, $${\mathcal{D}}_{\tau }^{{\epsilon }_{2},{\tau }_{2}}$$ and $${\mathcal{D}}_{\tau }^{{\epsilon }_{3},{\tau }_{3}}$$, respectively, are used in the non-linear mathematical model of convective fluid motion in rotating cavity. The numerical algorithms have been generated in terms of newly presented fractal–fractional differential operators on the basis of Adams–Bashforth method to compute the approximate solutions explicitly. The equilibrium points and stability analysis of the fractal–fractional Atangana–Baleanu, Caputo–Fabrizio and Caputo differential operators in Caputo sense have been investigated for non-linear mathematical model of convective fluid motion in rotating cavity. The numerical solutions are simulated in three types of variations (i) presence of fractional parameter without fractal parameter, (ii) presence of fractal parameter without fractional parameter, and (iii) presence of fractal parameter as well as fractional parameter. The chaotic behavior of convective fluid motion in rotating cavity based on each fractal–fractional differential operator has been highlighted as (a) projection on the x–y plane, (b) projection on the x–z plane, (c) projection on the y–z plane and (d) projection on the $$xyz$$ plane in three dimensions.

The paper discusses the dynamic behavior of a double mathematical pendulum with identical parameters of links and end loads, which is under the influence of viscous friction in both of its joints with generally different dissipative coefficients. A linear mathematical model of the system motion for small deviations is given, and a characteristic equation containing two dimensionless dissipative parameters is derived. For the case of low damping, approximate analytical expressions are found that make it possible to evaluate and compare with each other the damping factors during the motion of the system on each of the oscillation modes. A diagram of dissipative motion regimes is constructed, which arises when the plane of dimensionless parameters is divided by discriminant curves into regions with a qualitatively different character of the system motion. It is noted that a dissipative internal resonance can take place in the system under consideration, and the conditions for its existence in an analytical form are established, as well as their graphic illustration is also given. This article is the first part of the study of the dynamics of a dissipative double pendulum, the continuation of which will be presented as a separate work “Dynamics of a double pendulum with viscous friction in the joints. II. Dissipative oscillation modes and optimization of damping parameters”.

The article presents the results of an analysis of the parametric identification process of typical mathematical models of a brushless DC motor with an electronic commutator (BLDC) in off-line conditions. The aim of the analysis was to examine the impact of changes in motor load and power supply conditions on the obtained parameter values of mathematical models. The experiments used a nonlinear and linear mathematical model of the BLDC motor drive system in the form of a system of differential equations of individual phases of the BLDC motor electric circuit and a differential equation of the input variable in the form of supply voltage and the output variable in the form of angular velocity, respectively. The identified parameters of the mathematical models were determined on the basis of electrical and mechanical measurements of the motors’s output values when excited with various stator voltage values (in relative units). The Nelder-Mead numerical static optimization method was used to identify the nonlinear and linear mathematical model of the motor. The identified model parameters were determined for various operating conditions of the drive system with an inertial mass load and a hydraulic pump operating in a power drive system with a proportional valve. The motor load torque in the hydraulic system was obtained by using the throttling method by changing the pressure and flow parameters of the working medium. The influence of supply voltage and load torque on the static and dynamic properties of the motor was also analysed. The assessment of the convergence of the time responses of the drive system recorded in experiments and obtained from the solution of mathematical models was carried out on the basis of the correlation function. Laboratory tests were carried out in a drive system with motor BLDC of power 2.5 kW operating in a drive system with a piston pump.

A novel nonlinear modeling for the prediction of blast-induced airblast using a modified conjugate FR method

An important method for finding the optimal solution for linear and nonlinear models is the graphical method, which is used if the linear or nonlinear mathematical model contains one, two, or three variables. The models that contain only two variables are among the most models for which the optimal solution has been obtained graphically, whether these models are linear or non-linear in references and research that are concerned with the science of operations research, when the data of the issue under study is classical data. In this research, we will present a study through, which we present the graphical method for solving Neutrosophical nonlinear models in the following case: A nonlinear programming issue, the objective function is a nonlinear function, and the constraints are linear functions. Note that we can use the same method if (i) the objective function follower is a linear follower and the constraints are nonlinear; (ii) the objective function is a non-linear follower and the constraints are non-linear. In the three cases, the nonlinear models are neutrosophic, and as we know, the mathematical model is a nonlinear model if any of the components of the objective function or the constraints are nonlinear expressions, and the nonlinear expressions may be in both. At the left end of the constraints are neutrosophic values, at least one or all of them. Then, the possible solutions to the neutrosophic nonlinear programming problem are the set of rays NX ∈ Rn that fulfills all the constraints. As for the region of possible solutions, it is the region that contains all the rays that fulfill the constraints. The optimal solution is the beam that fulfills all constraints and at which the function reaches a maximum or minimum value, depending on the nature of the issue under study (noting that it is not necessary to be alone).